In the publication "Three-Dimensional Sensing of Rough Surfaces by Coherence Radar" by T. Dressel, G. Hausler, V. Venzke; Appl. Opt., Vol. 3, No. 7, of Mar. 1, 1992, an interferometric measuring device of this kind is described. This publication describes an interferometer having a short-coherent light source and a piezo-driven reflector for measuring shapes of rough surfaces. In the measuring device, a first beam component, in the form of a light wave that is reflected by an object to be measured, and a second beam component, in the form of a reference wave, are superimposed. The two light waves have a very short coherence length (a few .mu.m) so that the interference contrast reaches a maximum when the optical path difference is zero. To change the light path of the reference wave, a reflecting element in the form of a piezo-driven reflector is provided. By comparing the position of the piezo-driven reflector with the time of the occurrence of the interference maximum, it is possible to determine the distance to the object to be measured. The exact determination of the position of the piezo-driven reflector requires relatively considerable outlay.